1. **State the problem:** Solve the linear equation $$\frac{5}{6} - 6w = \frac{1}{3}$$ for $w$. 2. **Isolate the term with $w$:** Subtract $\frac{5}{6}$ from both sides: $$\frac{5}{6} - 6w - \frac{5}{6} = \frac{1}{3} - \frac{5}{6}$$ which simplifies to $$-6w = \frac{1}{3} - \frac{5}{6}$$ 3. **Find a common denominator and subtract the fractions:** $$\frac{1}{3} = \frac{2}{6}$$ so $$\frac{2}{6} - \frac{5}{6} = \frac{2 - 5}{6} = \frac{-3}{6} = -\frac{1}{2}$$ Thus, $$-6w = -\frac{1}{2}$$ 4. **Divide both sides by $-6$ to solve for $w$:** $$w = \frac{-\frac{1}{2}}{-6} = \frac{\cancel{-1}}{2} \times \frac{\cancel{-1}}{6} = \frac{1}{12}$$ 5. **Final answer:** $$w = \frac{1}{12}$$